theorem
  L is modular implies latt (L,P) is modular
proof
  assume
A1: for a,b,c being Element of L st a [= c holds a"\/"(b"/\"c) = (a"\/"b
  )"/\"c;
  let a9,b9,c9 be Element of latt (L,P);
  reconsider a = a9, b = b9, c = c9, bc = b9"/\"c9, ab = a9"\/"b9 as Element
  of L by Th68;
  assume a9 [= c9;
  then
A2: a [= c by Th74;
  thus a9"\/"(b9"/\"c9) = a"\/"bc by Th73
    .= a"\/"(b"/\"c) by Th73
    .= (a"\/"b)"/\"c by A1,A2
    .= ab"/\"c by Th73
    .= (a9"\/"b9)"/\"c9 by Th73;
end;
